Bottom Step Research Articles

Hydrodynamic performance of windsurfing boards with bottom modifications at high speed in calm water

Hydrodynamic performance of windsurfing boards is greatly affected by geometrical details of their bottom surfaces. In this study, computational fluid dynamics is applied to simulate flow around boards with several bottom modifications, including deadrise, rocker, step, wedge, and wing-tail profile. These simulations are conducted in steady-state, calm-water regimes at high planing speeds. It is found that at similar board trim angles and vertical positions, the largest lift is produced by setups with the bottom wedge and the wing-tail profile that enhance the downward deflection of the incident water flow. The highest lift-drag ratio is achieved by the variants with the bottom step and wedge that enable partial air ventilation of the bottom surface, which leads to reduced wetted surface and lower frictional resistance. The center of lift is located more forward on the rocker and stepped configurations, while it is positioned more rearward for the wedge and wing-tail setups. The obtained results can be used for guiding board designs aimed at maximizing the board hydrodynamic performance in calm water.

Scattering of gravity-capillary waves on a bottom step

Under the linear approximation, we study the scattering of gravity-capillary waves on a bottom step. The boundary conditions can be satisfied by considering a countable number of evanescent modes that are localized near the bottom step. Such modes have certain specific features compared to similar modes for pure gravity waves. In particular, there exists an extra mode. When a numerical solution is calculated, this extra mode allows us to match in the fluid region and impose the additional condition at the surface, which arises for capillary gravity waves (and not for pure gravity waves). The approximate formulas are suggested for the transformation coefficients. By means of numerical calculations, we find the reflection and transmission coefficients of traveling waves and compare the results with the predictions of the approximate formulas. The approximate formulas are shown to agree well with the numerical data. Both numerical and approximate results agree with the energy flux conservation. We also study the wave transformation on the rectangular underwater bump and trench, which are straightforward extensions of our step calculations. We calculate the transformation coefficients numerically and illustrate the transformation by time-dependent results, which are also shown as animations in the supplementary material.

Time-dependent flexural gravity wave scattering due to uneven bottom in the paradigm of blocking dynamics

The present study investigates the scattering of flexural gravity waves due to uneven bottom topography in the context of wave blocking. Emphasis is given to analyzing the effects of multiple propagating wave modes on the solution procedures. The mathematical model is developed for two scenarios: a bottom step and a submerged rectangular breakwater. For the bottom step case, the complete solution in terms of the velocity potential is obtained using the eigenfunction expansion method. Subsequently, the solution associated with the wave transformation by the bottom step is extended to the case of a submerged rectangular breakwater using symmetry characteristics of the velocity potential. The energy balance relation is derived in both cases using the conservation of energy flux in the presence of multiple propagating wave modes. Wave blocking occurs for four different frequencies in both the cases of the bottom step and the submerged breakwater due to variations in water depth. This makes the problem more complex as, depending on the frequency, multiple propagating wave modes can exist in either the reflected region, the transmitted region, or both. The transmitted wave amplitude associated with the lower wavenumber within the blocking frequencies exceeds unity, and this excess energy is balanced by the corresponding energy transfer rate. Additionally, removable discontinuities are observed at the blocking frequencies in the scattering coefficients, where group velocity ceases. In the context of floating ice sheets, the deflection is analyzed in the time domain for frequencies within and outside the blocking limits.

Transformation of a fully nonlinear breather-like package of internal waves over a bottom step in a layered fluid

In this paper, we study the process of transformation of a localized wave packet over a bottom step in a three-layer fluid, in which the height of the step is equal to or exceeds the thickness of the lower layer; therefore, density stratification becomes two-layer in the shallow water zone. In numerical experiments, both the height of the step and the width of the step were varied. The problem is solved in the framework of a fully nonlinear model of hydrodynamics of an inviscid incompressible stratified fluid. The primary analysis consisted in estimating the values of dimensionless parameters used, as a rule, in runup problems: the Froude and Iribarren numbers, the ratio of the characteristic wavelength to the characteristic slope width, the ratio of the topographic slope to the characteristic wave beam angle. Since the “cutoff” line for the lower pycnocline is partially or completely located on a step, one could expect the effects of run-up, breaking or reflection of waves propagating along the lower pycnocline, but this doesn’t happen. It is shown that the reflection of the wave packet from the step is minimal in all cases considered, a strong steepening of the wave is observed, but no breaking occurs in this case — the wave then just quickly decays on the lower pycnocline. An analysis of the spectral amplitudes and energy fields allows us to conclude that there is a transfer of energy from the lower pycnocline to the upper one. The breather in a two-layer fluid cannot exist, but the wave packet formed in the upper pycnocline after its destruction has much higher energy than it has before the step.

Numerical Investigation of Bottom Step Height Effect on The Hydrodynamic Performance of High-Speed Planing Crafts

Numerical Investigation of Bottom Step Height Effect on The Hydrodynamic Performance of High-Speed Planing Crafts

On the flow unsteadiness and operational characteristics of a novel supersonic fluidic oscillator

A novel supersonic jet oscillating method is investigated both experimentally and numerically. A rectangular primary supersonic jet is issued into a confined chamber with sudden enlargement. Secondary control jets are issued from the top and bottom backward-facing step regions formed due to sudden enlargement. The primary jet is oscillated in the transverse direction by blowing the secondary jets in the streamwise direction in a pulsating manner with a phase shift. The out-of-phase secondary jet blowing causes the primary jet to periodically adhere to the upper and lower part of the confined chamber, causing flapping of the primary jet and acting as a supersonic fluidic oscillator. The supersonic jet oscillation characteristics are experimentally investigated using shadowgraph type flow visualization technique and steady and unsteady pressure measurements. Quantitative analysis of the shadowgraph images using the construction of y – t and y – f plots reveals the presence of periodic jet oscillation with a discrete dominant frequency similar to the secondary jet excitation frequency. The existence of linearity between the excitation frequency and the flapping jet frequency on the low-frequency (0.66–6.6 Hz) side is first proven experimentally. Later, the high-frequency (16.67–5000 Hz) operation extent of the supersonic fluidic oscillator is further demonstrated using unsteady computational studies owing to the existing experimental facility's limitations. A reduced-order analytical framework has also been proposed to investigate the limiting oscillation frequency. It is found that the limiting frequency predicted from the proposed analytical model shows fairly good agreement with the computationally predicted results (5 kHz).

Research on the Stability of the Spacer Fluid Interface in Dual-Layer Pipe Dual-Gradient Drilling

Dual-layer pipe dual-gradient drilling technology is an emerging technology for solving the problem of the narrow safety density window in deepwater drilling. The unstable spacer fluid interface in this technology directly affects the dual-gradient pressure system in the annulus, causing changes in the drilling mud performance and affecting the control of bottom hole pressure and rock removal with drilling mud. Therefore, the key to the stable operation of dual-layer pipe dual-gradient drilling technology is to maintain the stability of the spacer fluid interface. Based on this, a seawater-spacer fluid-drilling mud annular flow model was established in this study, with a bottom hole pressure control step of 0.2 MPa, and the spacer fluid height after a single control was used as the evaluation index to study the influence of annular flow velocity, the spacer fluid properties, and the drill string rotation speed on the stability of the spacer fluid interface. The results show that in the determined conditions of the seawater and drilling mud system, the annular fluid flow rate and the physical parameters of the spacer fluid are the main factors affecting the stability of the spacer fluid interface. When the annular fluid flow rate increased within the range of 0.04~0.2 m/s, the liquidity index of the spacer fluid increased between 0.5 and 0.9, the consistency coefficient increased in the range of 0.6 to 1.4 Pa⋅sn, and the stability of the spacer fluid interface decreased. However, the stability of the spacer fluid interface increased with the increase in its density in the range of 1100~1500 kg/m3. The results obtained in this study can provide a reference for selecting the operating parameters to ensure the stable operation of dual-gradient pressure systems.

The exact Riemann Solver to the Shallow Water equations for natural channels with bottom steps

The Shallow Water equations model is commonly used to reproduce a wide variety of environmental flows. Its applications include river hydraulics and flood forecasting.Therefore, an algorithm to solve the Riemann problem for the Shallow Water equations can be a considerable asset for the development of numerical schemes devoted to the solution of such equations. Nevertheless, for real world applications, it becomes mandatory to consider the influence of the irregular shape of the cross section of natural channels in the solution.This work presents an energy based exact Riemann solver for the Shallow Water equations for channels with an arbitrarily shaped cross section with the presence of a non flat bottom and dry states.The procedure for solving the Riemann problem involves the solution of a system of non linear algebraic equations, for which a CPU time efficient solution strategy based on nested Newton-Raphson methods is presented.The proposed solver can be used to develop Finite Volume or Discontinuous Galerkin schemes, based on the Godunov method. For a non flat bottom, the Shallow Water equations are a non conservative system, once the bottom elevation is included in the state variables. Many available schemes take advantage of this fact to use approximate path-conservative Riemann solvers. In other cases, the term related to the non flat bottom is treated as a source term. The use of this exact solver avoids the necessity of considering the bottom topography as a source term and of reverting to approximate solvers. These strategies can in facts pose numerical problems in situations such as transonic rarefactions and flows approaching abrupt changes in bottom topography.The solver is tested by reproducing the solution of Riemann problems with a Godunov finite volume scheme. An analysis of the performance of the solver shows that it requires less computational time than path-conservative schemes and that it has better stability and convergence properties, especially in situations involving resonant waves, such as transonic flows across a bottom step.

Active Flow Control of Supersonic Jet Using Streamwise Pulsed Blowing

The present study investigates a novel control strategy to create a sweeping oscillatory jet using fluidic actuation principle. A supersonic underexpanded primary jet issued into a suddenly expanding duct is oscillated by giving cyclic pulsed secondary jet blowing in the top and bottom step regions of the suddenly expanding duct. The current study employs the bistable nature of jet expansion seen in a suddenly expanding duct for the jet oscillation. The cyclic perturbations (pulsed secondary jet blowing) given in the streamwise direction switch the direction of the asymmetric jet expansion of the underexpanded primary supersonic jet to the top and bottom wall alternatively, thereby creating an oscillatory supersonic jet. It is found that the switching of the direction of the primary jet to any one wall is caused by the Coanda effect produced by the secondary jet issued in the corresponding wall side. The results show that the primary jet quickly responds to the secondary jet perturbations and that the supersonic primary jet oscillation frequency nearly matches secondary jet perturbation frequency. A parametric study to investigate the jet oscillation characteristics with various secondary jet oscillation frequencies and mass flow rate ratios are also being carried out in the present study. It is found that the jet oscillation frequency increases with increase in the secondary jet pulsation frequency. The jet deflection is found to increase with increase in the secondary jet to primary jet mass flow ratio (blowing ratio) up to a critical limit, after which the increment in jet deflection ceases due to the restrictions imposed by the duct geometry.

Transformation of envelope solitons on a bottom step

In this paper, we study the transformation of surface envelope solitons traveling over a bottom step in water of a finite depth. Using the transformation coefficients earlier derived in the linear approximation, we find the parameters of transmitted pulses and subsequent evolution of the pulses in the course of propagation. Relying on the weakly nonlinear theory, the analytic formulas are derived which describe the maximum attainable wave amplitude in the neighborhood of the step and in the far zone. Solitary waves may be greatly amplified (within the weakly nonlinear theory formally, even without a limit) when propagating from relatively shallow water to the deeper domain due to the constructive interference between the newly emerging envelope solitons and the residual quasi-linear waves. The theoretical results are in good agreement with the data of direct numerical modeling of soliton transformation. In particular, more than double wave amplification is demonstrated in the performed simulations.

The next step in optimising the stair horizontal-vertical illusion: Does a perception-action link exist in older adults?

Tripping on stairs results from insufficient foot to step edge clearance and can often lead to a fall in older adults. A stair horizontal-vertical illusion is suggested to increase the perceived riser height of a step and increase foot clearance when stepping up. However, this perception-action link has not been empirically determined in older adults. Previous findings suggesting a perception-action effect have also been limited to a single step or a three-step staircase. On larger staircases, somatosensory learning of step heights may be greater which could override the illusory effect on the top step. Furthermore, the striped nature of the existing stair horizontal-vertical illusion is associated with visual stress and may not be aesthetically suitable for use on public stairs. These issues need resolving before potential future implementation on public stairs. Experiment 1. A series of four computer-based perception tests were conducted in older (N=14: 70±6years) and young adults (N=42: 24±3years) to test the influence of different illusion designs on stair riser height estimation. Participants compared images of stairs, with horizontal-vertical illusions or arbitrary designs on the bottom step, to a plain stair with different bottom step riser heights and selected the stair they perceived to have the tallest bottom riser. Horizontal-vertical illusions included a previously developed design and versions with modified spatial frequencies and mark space ratios. Perceived riser height differences were assessed between designs and between age groups. Experiment 2. To assess the perception-action link, sixteen older (70±7years) and fifteen young (24±3years) adults ascended a seven-step staircase with and without horizontal-vertical illusions tested in experiment 1 placed onto steps one and seven. Foot clearances were measured over each step. To determine whether changes in perception were linked to changes in foot clearance, perceived riser heights for each horizontal-vertical illusion were assessed using the perception test from experiment 1 before and after stair ascent. Additional measures to characterise stair safety included vertical foot clearance, margins of stability, foot overhang, stair speed, and gaze duration, which were assessed over all seven steps. Experiment 1. All horizontal-vertical illusion designs led to significant increases in the perceived riser height in both young and older adults (12-19% increase) with no differences between age groups. Experiment 2. On step 7, each horizontal-vertical illusion led to an increase in vertical foot clearance for young (up to 0.8cm) and older adults (up to 2.1cm). On step 1 significant increases in vertical foot clearance were found for a single horizontal-vertical illusion when compared to plain (1.19cm increase). The horizontal-vertical illusions caused significant increases in the perceived riser height (young; 13% increase, older; 11% increase) with no differences between illusion design, group or before and after stair ascent. No further differences were found for the remaining variables and steps. Results indicate a perception-action link between perceived riser height and vertical foot clearance in response to modified versions of the horizontal-vertical illusion in both young and older adults. This was shown with no detriment to additional stair safety measures. Further evaluating these illusions on private/public stairs, especially those with inconsistently taller steps, may be beneficial to help improve stair safety for older adults.

Experimental study on transformation and energy properties of depression internal solitary wave over a bottom step

Waveform deformation and breaking are widespread phenomena when internal solitary waves (ISWs) encounter changing topographies, which have been observed in many parts of oceans. In this study, experiments are performed in a series of combinations of bottom step topographies with different heights and ISWs in different amplitudes within a two-layer stratified fluid system. According to experimental results, the evolution processes of ISWs over the bottom step are classified into four typical regimes as the wave–step interaction varying from weak to strong, which are the transmission regime, transitional regime, breaking regime, and reflection regime, corresponding to the evolution patterns of steady passage, deformation, breaking, and strong reflection, respectively. To describe the intensity of wave–step interaction, a new improved interaction parameter is proposed, which takes both relative amplitude of ISWs and relative topography changes into consideration, and achieved better effectiveness in defining the boundaries between different regimes. In terms of energy properties, with the wave–step interaction becoming stronger, the transmission ratio keeps decreasing throughout all regimes, while the reflection wave starts to appear since the breaking regime and its energy keeps increasing. At the critical point between the breaking regime and reflection regime, the reflection ratio equals the transmission ratio, and the energy loss ratio reaches its maximum.

Model Based Assessment of the Reflection Behavior of Tidal Waves at Bathymetric Changes in Estuaries

Estuaries are often modified by human activities. Adjustments in the morphology of an estuary have a potential impact on the hydrodynamics and on the reflection behavior of the tide. The influence of such system changes on the complex tidal regime with a large number of superimposed tidal constituents is not fully understood yet. The reflection properties of estuaries that are characterized by abrupt changes in geometry are systematically investigated on the basis of simplified estuary model approaches to improve the understanding of the oscillation and reflection behavior of tidal waves in estuaries. The reflection coefficients at abrupt cross-sectional changes are determined by two different methods, i.e., an analytical energy-based approach and a hydrodynamic numerical (HN) model. Comparisons indicate a high agreement of the results of the different methods when evaluating the reflection coefficient. The tidal constituents are reflected at partial and total reflectors and amplified by shoaling depending on the water depths, the height of the bottom step and the horizontal constriction. A harmonic analysis of simulated water level data partly shows the formation and amplification of higher harmonic components as a result of shallow water effects. The interaction with reflectors results in an increasing amplification of the tidal constituents and the tide.

О новом методе регуляризации уравнений двухфазной несжимаемой среды

This paper presents a new method for the numerical simulation of two-phase incompressible immiscible flows. The methodology is based on the hydrodynamic equations regularization method using the quasi-hydrodynamic approach. Two systems of regularized equations are developed, which differ in terms of velocity regularization. The comparison of the described equations systems and the approbation of the numerical model on two numerical tests are given: dam break problem with the bottom step, for which the experimental data are described (Koshizuka’s experiment), and the cubic drop evolution problem. The latter problem is a model one with artificially specified parameters that demonstrates the effects of surface tension. A numerical model of two-phase flows is implemented in the open-source platform OpenFOAM using the finite volume method.

Interaction of the elementary waves for shallow water equations with discontinuous topography

The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears when the water depth changes, especially when there exists a bottom step. In this paper, we are mainly concerned with the interaction between a stationary wave with either a shock wave or a rarefaction wave. By using the characteristic analysis methods, the evolution of waves is described during the interaction process. The solution in large time scale is also presented in each case. The results may contribute to research on more complicated wave interaction problems.

Simulation of Convective Heat Transfer in 3D Forward Facing Step Using Various Turbulence Models

In this work, a modified solver from the OpenFOAM 4.1 software was used to study the fluid flow and heat transfer characteristics over a forward facing step (FFS) considering various turbulence models, viz., k-e , k-ω , k-ω SST and v 2 -f . Numerical computations were performed using a newly developed transient solver, pisoTempFoam. Modeling and meshing of the geometry and setting of the boundary conditions were done with OpenFOAM. The bottom (upstream, step and downstream) walls were heated at a constant temperature of 350K, while the fluid inlet temperature was 298K. The simulation results were compared with those available in the literature. Variation of skin friction coefficient ( C f ), coefficient of pressure ( C p ), and Nusselt number (Nu) for different Reynolds numbers (Re), contraction ratios (CR) and different fluids are presented. This article also presents information about recirculation bubbles in the upstream and downstream regions of the FFS. The results show that the combined effect of turbulence models and parameters, such as CR, Re and Pr, change the flow and heat transfer characteristics of the FFS. The present CFD simulation plays a pivotal role in the analysis of flow over airfoils at a large angle of attack in heat exchangers and pipes whose area suddenly changes.

Bottom step enlarging horizontal momentum flux of dam break flow

Dam break flow over the horizontal bed with a bottom step is solved using both computational fluid dynamics and shallow water equation models. The bottom step is a scenario related to greenwater overtopping of offshore structures, in which a sharp variation of water depth exists from the location in front of the ship to the position on deck. The effect of bottom step level on the horizontal momentum flux of dam break flow, representative of its impact loading on plate-type structures, is investigated. Both these models predict a trend that the increase of bottom step level leads to an increase of the maximum horizontal momentum flux, being larger than that of the classical dam break solution. The increasing rate is large for a small bottom step level but becomes less sensitive for a large bottom step level. This trend can be attributed to the fact that the rarefaction wave associated with draw down of water upstream of the dam travels faster with a bottom step.

Sequential optimization of the geometrical parameters of an OWC device based on the specific wave characteristics

Conventional Wave Energy Converters (WECs) are designed to extract the wave energy from the oceans with the wave power of 20–50 kW-per-meter. If these WECs are used where the wave energy is less than the mentioned values they cannot work in their maximum performance. Therefore it is proposed to optimize the WECs for the average wave power in each place. In this research, an Oscillating Water Column (OWC) is investigated to extract the maximum output power based on the characteristics of the Faroor island waves in the Persian Gulf. The average power of the Persian Gulf Waves is less than 10 kW-per-meter and using a conventional wave energy converter is not efficient. Numerical simulation is performed using ANSYS-Fluent software. In this study, waves are generated using nonlinear second order stokes theory. Also, the k- ω turbulence model and volume of fluid scheme are used for turbulence modeling and interface tracking respectively. Finally, with optimizing each parameter an optimum geometry with an efficiency of 41.5% is obtained to extract the Faroor Island waves’ energy. This study emphasizes on this fact that one should design a new geometry to reach the best performance of the OWC in new wave characteristics. • The optimized OWC dimensionless parameters change with wave characteristics. • The optimized OWC increases the efficiency from 19.75% to 41.5%. • The bottom step can increase the hydrodynamic efficiency of the OWC. • The best length of the bottom step is equal to one wavelength. • The best front angle of the bottom step is 90 degrees.

The Stair Climb Power Test

The Stair Climb Power Test

Experimental study for the breaking properties of internal solitary waves flowing over a bottom step

The breaking properties of internal solitary waves (ISWs) flowing over a bottom step were investigated experimentally. The experiments were performed in a two-layer immiscible system to avoid the influence of diffusion and mixing. The flat bottom condition and the bottom step condition had been conducted respectively. The characteristics of incident ISWs, the process of breaking and the subsequent developments were taken into discussion. A modified internal Iribarren number was introduced, and the critical condition of breaking was considered to be related to its trend change point. The initial stage of the breaking process was found can be divided into spatially discrete characteristic structures other than messy flowing of the full interface. And the characteristic structures have close horizontal lengths for different amplitudes. The horizontal velocity gradient was identified as the key parameter of shear instability. By analyzing the subsequent developments, the completely broken ISWs were found can reform a quasi ISWs propagating upon the bottom step which has a smooth front-face and an ever-breaking back-face. Due to the breaking of the back-face, the amplitude of reformed ISWs continues to decrease. Meanwhile, the attenuation rate was noticed to be related to the incident amplitude, but not be related to whether it is broken or the degree of breaking.